“Money, says the proverb, makes money. When you have a little, it is often easier to get more. The great difficulty is to make that little.”
A. Smith, The Wealth of Nations, Chapter XI, p. 111.
Abstract
We study a model of wealth accumulation in altruistic lineages, in which households face uninsurable risk, investment indivisibilities and borrowing constraints. A thick upper tail of the stationary distribution of wealth is shown to emerge as a robust prediction, irrespective of (1) the presence of multidimensional (wealth and ability) heterogeneity and non-convexities in human capital formation, and (2) the nature of parental bequest motives (joy-of-giving vs. paternalism). Additionally, (3) we identify conditions under which the unique, ergodic wealth distribution exhibits a mass point at the bottom of its support, where credit market imperfections continue to affect, along the convergence process, the structure of wealth transitions at the lineage level. Motivated by these results, we then analyze the sensitivity of the left tail to various frictions and fiscal instruments that affect bequest strategies and the ensuing transmission of wealth across generations. In particular, capital income or bequest taxes with no redistribution may reinforce economic mechanisms underpinning mobility traps in the left tail, thereby increasing the persistence of households in the lowest tiers of the wealth distribution.
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References
Aiyagari, S.R.: Uninsured idiosyncratic risk and aggregate saving. Q. J. Econ. 109(3), 659–684 (1994)
Andreoni, J.: Impure altruism and donations to public goods: a theory of warm-glow giving. Econ. J. 100(401), 464–477 (1990)
Balestra, C., Tonkin, R.: Inequalities in household wealth across OECD countries: evidence from the OECD wealth distribution database (2018)
Bastani, S., Waldenström, D.: How should capital be taxed? J. Econ. Surv. 34(4), 812–846 (2020)
Becker, G.S., Tomes, N.: An equilibrium theory of the distribution of income and intergenerational mobility. J. Polit. Econ. 87(6), 1153–1189 (1979)
Becker, G.S., Tomes, N.: Human capital and the rise and fall of families. J. Law Econ. 4(3, Part 2), S1–S39 (1986)
Benabou, R.: Heterogeneity, stratification, and growth: macroeconomic implications of community structure and school finance. Am. Econ. Rev. 86(3), 584–609 (1996)
Benhabib, J., Bisin, A., Zhu, S.: The distribution of wealth and fiscal policy in economies with finitely lived agents. Econometrica 79(1), 123–157 (2011)
Benhabib, J., Bisin, A., Zhu, S.: The wealth distribution in Bewley economies with capital income risk. J. Econ. Theory 159, 489–515 (2015)
Benhabib, J., Bisin, A., Luo, M.: Wealth distribution and social mobility in the US: a quantitative approach. Am. Econ. Rev. 109(5), 1623–1647 (2019)
Bewley, T.: The permanent income hypothesis: a theoretical formulation. J. Econ. Theory 16(2), 252–292 (1977)
Bewley, T.: A difficulty with the optimum quantity of money. Econometrica J. Econ. Soc. 1485–1504 (1983)
Birkner, M., Scheuer, N., Wälde, K.: The dynamics of Pareto distributed wealth in a small open economy. Econ. Theor. 76(2), 607–644 (2023)
Blinder, A.S.: Intergenerational transfers and life cycle consumption. Am. Econ. Rev. 66(2), 87–93 (1976)
Cao, D., Luo, W.: Persistent heterogeneous returns and top end wealth inequality. Rev. Econ. Dyn. 26, 301–326 (2017)
Castaneda, A., Diaz-Gimenez, J., Rios-Rull, J.-V.: Accounting for the us earnings and wealth inequality. J. Polit. Econ. 111(4), 818–857 (2003)
Champernowne, D.G.: A model of income distribution. Econ. J. 63(250), 318–351 (1953)
Charles, K.K., Hurst, E.: The correlation of wealth across generations. J. Polit. Econ. 111(6), 1155–1182 (2003)
Chetty, R., Hendren, N., Kline, P., Saez, E.: Where is the land of opportunity? The geography of intergenerational mobility in the United States. Q. J. Econ. 129(4), 1553–1623 (2014)
D’Amato, M., Di Pietro, C.: Occupational mobility and wealth evolution in a model of educational investment with credit market imperfections. J. Econ. Inequal. 12, 73–98 (2014)
Davies, J.B., Shorrocks, A.F.: The distribution of wealth. Handb. Income Distrib. 1, 605–675 (2000)
Dávila, J.: Bequests or education. Econ. Theor. 75(4), 1039–1069 (2023)
De Nardi, M.: Wealth inequality and intergenerational links. Rev. Econ. Stud. 71(3), 743–768 (2004)
De Nardi, M., Fella, G.: Saving and wealth inequality. Rev. Econ. Dyn. 26, 280–300 (2017)
Diamond, P.: Social security. Am. Econ. Rev. 94(1), 1–24 (2004)
Diamond, P., Geanakoplos, J.: Social security investment in equities. Am. Econ. Rev. 93(4), 1047–1074 (2003)
Durlauf, S.N.: A theory of persistent income inequality. J. Econ. Growth 1, 75–93 (1996)
Dutta, J., Michel, P.: The distribution of wealth with imperfect altruism. J. Econ. Theory 82(2), 379–404 (1998)
Dynan, K.E., Skinner, J., Zeldes, S.P.: Do the rich save more? J. Polit. Econ. 112(2), 397–444 (2004)
Fagereng, A., Holm, M.B., Moll, B., Natvik, G.: Saving behavior across the wealth distribution: the importance of capital gains. Technical report, National Bureau of Economic Research (2019)
Flavin, M., Yamashita, T.: Owner-occupied housing and the composition of the household portfolio. Am. Econ. Rev. 92(1), 345–362 (2002)
Galor, O., Zeira, J.: Income distribution and macroeconomics. Rev. Econ. Stud. 60(1), 35–52 (1993)
Gollier, C.: The Economics of Risk and Time. MIT Press, Cambridge (2001)
Grossmann, V., Poutvaara, P.: Pareto-improving bequest taxation. Int. Tax Public Finance 16, 647–669 (2009)
Heckman, J.J., Stixrud, J., Urzua, S.: The effects of cognitive and noncognitive abilities on labor market outcomes and social behavior. J. Law Econ. 24(3), 411–482 (2006)
Henderson, D.J., Polachek, S.W., Wang, L.: Heterogeneity in schooling rates of return. Econ. Educ. Rev. 30(6), 1202–1214 (2011)
Jappelli, T., Pistaferri, L.: The Economics of Consumption: Theory and Evidence. Oxford University Press, Oxford (2017)
Kesten, H.: Random difference equations and renewal theory for products of random matrices. Acta Math. 131(1), 207–248 (1973)
Kimball, M.: Precautionary saving in the small and in the large. Econometrica 58(1), 53–73 (1990)
Klass, O.S., Biham, O., Levy, M., Malcai, O., Solomon, S.: The Forbes 400, the pareto power-law and efficient markets. Eur. Phys. J. B 55(147), 143 (2007)
Kopczuk, W.: Incentive effects of inheritances and optimal estate taxation. Am. Econ. Rev. 103(3), 472–477 (2013)
Krusell, P., Smith, A.A.: Quantitative macroeconomic models with heterogeneous agents. Econom. Soc. Monogr. 41, 298 (2006)
Loury, G.C.: Intergenerational transfers and the distribution of earnings. Econometrica (1981)
Ma, Q., Stachurski, J., Toda, A.A.: The income fluctuation problem and the evolution of wealth. J. Econ. Theory 187, 105003 (2020)
Marshall, A.: The principles of economics. Technical Report, McMaster University Archive for the History of Economic Thought (1890)
Meyn, S., Tweedie, R.L.: Markov Chains and Stochastic Stability. Cambridge University Press, Cambridge (2009)
Mirek, M.: Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps. Probab. Theory Relat. Fields 151(3), 705–734 (2011)
Mookherjee, D., Napel, S.: Intergenerational mobility and macroeconomic history dependence. J. Econ. Theory 137(1), 49–78 (2007)
Mookherjee, D., Napel, S.: Welfare rationales for conditionality of cash transfers. J. Dev. Econ. 151, 102657 (2021)
Mookherjee, D., Ray, D.: Persistent inequality. Rev. Econ. Stud. 70(2), 369–393 (2003)
Moskowitz, T.J., Vissing-Jørgensen, A.: The returns to entrepreneurial investment: A private equity premium puzzle? Am. Econ. Rev. 92(4), 745–778 (2002)
Nirei, M., Aoki, S.: Pareto distribution of income in neoclassical growth models. Rev. Econ. Dyn. 20, 25–42 (2016)
Pareto, V.: Les systèmes socialistes, volume 2. V. Giard & e. Briere (1903)
Pestieau, P., Thibault, E.: Love thy children or money: reflections on debt neutrality and estate taxation. Econ. Theor. 50, 31–57 (2012)
Piketty, T.: Capital in the Twenty-First Century. Harvard University Press, Harvard (2014)
Ray, D.: On the dynamics of inequality. Econ. Theor. 29(2), 291–306 (2006)
Ray, D., Genicot, G.: Measuring upward mobility. Am. Econ. Rev. 113(11), 3044–3089 (2023)
Rothschild, M., Stiglitz, J.E.: Increasing risk II: its economic consequences. J. Econ. Theory 3(1), 66–84 (1971)
Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, Berlin (2007)
Stachurski, J., Toda, A.A.: An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity. J. Econ. Theory 182, 1–24 (2019)
Toda, A.A.: Wealth distribution with random discount factors. J. Monet. Econ. 104, 101–113 (2019)
Vermeulen, P.: How fat is the top tail of the wealth distribution? Rev. Income Wealth 64(2), 357–387 (2018)
Wan, J., Zhu, S.: Bequests, estate taxes, and wealth distributions. Econ. Theor. 67, 179–210 (2019)
Wolff, E.N.: Estimates of household wealth inequality in the US, 1962–1983. Rev. Income Wealth 33(3), 231–256 (1987)
Wolff, E.N.: 4. Changes in household wealth in the 1980s and 1990s in the united states. International Perspectives on Household Wealth, p. 107 (2006)
Zhu, S.: A Becker–Tomes model with investment risk. Econ. Theor. 67(4), 951–981 (2019)
Acknowledgements
We are grateful to an Associate Editor and two anonymous Reviewers for several comments and suggestions, which have helped us to greatly improve the manuscript. We also thank Achille Basile, Chetan Dave, Paula Gobbi (discussant), Tullio Jappelli, Dilip Mookherjee, Andy Newman, Jacques Silber, and Emma Tominey for insightful discussions on previous versions of the manuscript. We wish to thank seminar/conference participants (CFE 2018, IASI-CNR 2019, SAET Conference 2015 & 2019, University of Trento 2019, LOrde Workshop 2022, CefES Conference 2022, RCEA Conference 2022, RES Annual Conference 2022, PET Conference 2022, EWET 2022, SITES Conference 2022, CISEPS Annual Workshop 2023, SEHO 2023, ASSET 2023, University of Napoli Parthenope 2024, University of Alberta 2024, Inequality in Rome Seminar Series - Roma Tre University) for comments. Special gratitude we wish to express to Alberto Bisin for stimulating the questions addressed in this paper. Any remaining errors are our own.
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D’Amato, M., Di Pietro, C. & Sorge, M.M. Left and right: a tale of two tails of the wealth distribution. Econ Theory (2024). https://doi.org/10.1007/s00199-024-01581-w
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DOI: https://doi.org/10.1007/s00199-024-01581-w
Keywords
- Wealth distribution
- Wealth inequality
- Capital income risk
- Credit market imperfections
- Educational investment